The architecture of the neural network employed in this work is shown in Fig. REF . It consist of 3 layers with 2, 8 and 1 neurons in the input, hidden and output layers, respectively. Then, according to Eq. (REF ), there are 33 fitting parameters (24 weights and 9 biases) in our neural network. To optimize the fitting parameters of our network we employ the Adam algorithm [1]}, an extended version of the stochastic gradient descent method [2]}. The input dataset of our network consist of two features, the HO spacings \(\hbar \omega \)  and the maximum number of HO basis states \(N_{\max }\)  employed in the hypernuclear NCSM calculations of Refs. [3]}, [4]}, [5]}, and the corresponding target observable, namely, the \(\Lambda \)  separation energy of the light hypernuclei under study. We use the \(80\%\)  of the input dataset to train the network and leave the \(20\%\)  of it to test it. Since the available input dataset in our case is not too large (we have only 128 data points in the case of \(^3_\Lambda \) H and much less in the \(^4_\Lambda \) H and \(^4_\Lambda \) He cases, see Refs. [3]}, [4]}, [5]}), to avoid overfitting we enlarge it by performing a cubic spline interpolation in the HO spacing \(\hbar \omega \)  at each given value of \(N_{max}\)  of the original input dataset of Refs. [3]}, [4]}, [5]}. To further reduce the overfitting, we also introduce a Gaussian noise in the enlarged input dataset during the training of the network. Adding noise makes the network less able to memorize data patterns since they change randomly during all the training process and, consequently, overfitting is largerly reduced. The enlargement of the input dataset and the addition of noise are simple and economical ways to obtain more information from the limited amount of existing input data, making our basic single-hidden-layer network more robust. In addition, we have employed a \(10\%\)  of the training data subset to give an estimate of the network skill while tuning its hyperparameters (i.e., number of layers and neurons, activation function, optimizer algorithm, number of iterations during the training process, ...) to arrive to our final model. Note that this validation dataset is different from the test dataset which is used to give an unbiased estimate of the skill of the final tuned network.
